The volume of a cube is 216 cubic feet. What is the length of each side of the cube?

side = ? ? ? feet

To solve this problem, we can use the grating equation:

m * λ = d * sin(θ)

Where:

m is the order of the fringe

λ is the wavelength of light

d is the slit spacing (distance between adjacent slits)

θ is the angle of the fringe

In this case, we're given:

m = 3 (third-order fringe)

θ = 24.0°

We need to calculate the slit spacing (d) using the information that the grating has 3200 slits per cm. First, we convert the number of slits per cm to the slit spacing in meters:

slits per cm = 3200

slits per m = 3200 * 100 = 320,000

Now we can calculate the slit spacing (d):

d = 1 / (slits per m)

d = 1 / 320,000

Now, let's substitute the given values into the grating equation and solve for λ (wavelength):

m * λ = d * sin(θ)

3 * λ = (1 / 320,000) * sin(24.0°)

λ = (1 / (3 * 320,000)) * sin(24.0°)

Using a calculator, we can calculate the value of λ:

λ ≈ 5.79 × 10^(-7) meters or 579 nm

Therefore, the wavelength of light for which the grating with 3200 slits per cm produces a third-order fringe at a 24.0° angle is approximately 579 nm.

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Answer:

Hi! The answer to your question is [tex]3.05[/tex]

Step-by-step explanation:

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Hope this helps!!

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Answer:

Easy,

1) To find the area you need to multiply. Therefore 10 x 4 = 40 square centimeters.

2) 20, why? A calculator online for area of a triangle, it really helps! :) just look up triangle area in the future.

Step-by-step explanation:

Answer:

I have actually done this before, I got it right and I chose C!

hope this helps. love u guys!

Answer:

The 4th answer choice

Explain:

195 divided by 3 is 65. Then the diameter of 307 needs to be divided by 2 to get the radius. Now take the radius and square it to get 23562.25. Now times 3.14. Lastly, multiply by the 65 to get 4809055.225. Hope that helps! :)

Answer:

4

Step-by-step explanation:

We can do this problem by doing the absolute value of the difference between 2 and -2.

2-(-2)=4. Absolute value of 4 is 4.

Hope this helped.

~cloud

Answer:

4

Step-by-step explanation:

the number of favorable outcomes is 35 * 20475 = 716,625.

Probability = 716,625 / (35! / (7!(35 - 7)!)).

To determine the probability of winning the $10 prize by matching exactly three numbers, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes can be calculated using combinations. Since we are selecting 7 numbers out of 35, the total number of possible outcomes is given by the combination formula:

C(n, r) = n! / (r!(n - r)!)

In this case, n = 35 (total numbers) and r = 7 (numbers selected). Substituting these values into the formula:

C(35, 7) = 35! / (7!(35 - 7)!)
= 35! / (7!28!)

The number of favorable outcomes is determined by choosing 3 winning numbers from the 7 numbers selected and 4 non-winning numbers from the remaining 28 numbers. The number of favorable outcomes can be calculated using combinations as well:

C(7, 3) * C(28, 4)

Substituting the values into the formula:

C(7, 3) * C(28, 4) = (7! / (3!(7 - 3)!)) * (28! / (4!(28 - 4)!))

Calculating these values:

C(7, 3) = 7! / (3!(7 - 3)!)
= 7! / (3!4!)
= (7 * 6 * 5) / (3 * 2 * 1)
= 35

C(28, 4) = 28! / (4!(28 - 4)!)
= 28! / (4!24!)
= (28 * 27 * 26 * 25) / (4 * 3 * 2 * 1)
= 20475

Therefore, the number of favorable outcomes is 35 * 20475 = 716,625.

Now, we can calculate the probability of winning the $10 prize by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes
= 716,625 / C(35, 7)

Calculating this value:

Probability = 716,625 / (35! / (7!(35 - 7)!))

It is important to note that calculating the factorial of 35 might result in very large numbers, which may be computationally intensive. Alternatively, you can use numerical methods or estimation techniques to approximate the probability.

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Answer:

The arc length is about 12.57.

Step-by-step explanation:

Formula for arc length: 2πr( degrees/360)

For ours lets do 2π8(90/360)

Simplify the 90 and 360: 16π(1/4)

This gives you: 16π/4

Divide by 4

You get: 4π

4π ≅ 12.57

There are 28 different bit strings of length 8 that satisfy the condition of having two zeros that are never together.

To count the number of bit strings of length 8 with two zeros that are never together, we can use the concept of combinations.

First, let's consider the possible positions for the two zeros. The zeros cannot be adjacent to each other, which means they must be placed in non-adjacent positions in the string.

Since there are 8 positions in the string, we can choose 2 positions for the zeros in C(8, 2) ways. This gives us the number of ways to select the positions for the zeros.

Once we have chosen the positions for the zeros, the remaining 6 positions must be filled with ones. There is only one way to do this, as all the remaining positions will be filled with ones.

Therefore, the total number of bit strings of length 8 with two zeros that are never together is equal to C(8, 2) = 28.

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The test statistic for this problem is given as follows:

t = -0.7.

We have the standard deviation for the sample, hence the t-distribution is used to calculate the test statistic.

The equation for the test statistic is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 68.4, \mu = 69, s = 10.5, n = 152[/tex]

Hence the test statistic is given as follows:

[tex]t = \frac{68.4 - 69}{\frac{10.5}{\sqrt{152}}}[/tex]

t = -0.7.

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Answer:add 11 on both sides sorry

Answer: subtract 11 from both sides

Step-by-step explanation: this was an assigned assignment for me two days ago

The least nonnegative residue of 64!/52! modulo 13 is 4.

Wilson's theorem states that for any prime number 'p', the factorial of (p-1) is congruent to -1 modulo p. This can be written as (p-1)! ≡ -1 (mod p).

Using Wilson's theorem, we can find the least nonnegative residue modulo 89 for the integer 861.

For n = 861 and m = 89, we need to calculate (n mod m) as follows:

861 mod 89 = 861 - (89 * (861 // 89))

= 861 - (89 * 9)

= 861 - 801

= 60

Therefore, the least nonnegative residue of 861 modulo 89 is 60.

Now let's move on to the second part.

For n = 64!/52! and m = 13, we can simplify the expression using cancelation:

64!/52! = (64 * 63 * 62 * ... * 53 * 52!)/52!

Most of the terms in the numerator and denominator cancel out, leaving:

64 * 63 * 62 * ... * 53

To find the least nonnegative residue modulo 13, we can calculate the product of the remaining terms and take the result modulo 13.

(64 * 63 * 62 * ... * 53) mod 13 ≡ (11 * 12 * 1 * 2 * ... * 3) mod 13

≡ (11 * (-1) * 1 * 2 * ... * 3) mod 13

≡ (-11 * 1 * 2 * ... * 3) mod 13

Since (-11) ≡ 2 (mod 13), we have:

(-11 * 1 * 2 * ... * 3) mod 13 ≡ (2 * 1 * 2 * ... * 3) mod 13

Calculating the product, we find:

(2 * 1 * 2 * ... * 3) mod 13 ≡ 4 (mod 13)

Therefore, the least nonnegative residue of 64!/52! modulo 13 is 4.

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The approximate value of sin(theta) for 0 degrees < theta < 90 degrees, given cos(theta) = 0.3090, is approximately ±0.9511. The correct answer from the given options is A, which states sin(theta) = 0.9511 and tan(theta) = 0.3249.

To determine the value of sin(theta) given that cos(theta) is 0.3090, we can use the identity [tex]\(\sin^2(\theta) + \cos^2(\theta) = 1\)[/tex].

Since we know cos(theta) is 0.3090, we can substitute it into the identity:

[tex]\(\sin^2(\theta) + 0.3090^2 = 1\)[/tex]

[tex]\(\sin^2(\theta)\)[/tex] + 0.095481 = 1

[tex]\(\sin^2(\theta)\)[/tex] = 0.904519

Taking the square root of both sides, we get:

sin(theta) = √(0.904519)

sin(theta) ≈ ±0.9511

So, the approximate value of sin(theta) is approximately ±0.9511.

Now let's evaluate the given options:

A. sin(theta) = 0.9511; tan(theta) = 0.3249

B. sin(theta) = 0.9511; tan(theta) = 3.0780

C. sin(theta) = 3.2362; tan(theta) = 0.0955

D. sin(theta) = 3.2362; tan(theta) = 10.4731

We can eliminate options C and D immediately since the value of sin(theta) cannot be greater than 1.

Now, let's consider options A and B. Both options have sin(theta) = 0.9511, which matches our approximate value. However, the value of tan(theta) in option A is 0.3249, while in option B it is 3.0780.

Since we're looking for values of sin(theta) and tan(theta) that are consistent with the given cos(theta) = 0.3090, we can conclude that option A is the correct answer.

Therefore, the approximate values of sin(theta) and tan(theta) for 0 degrees < theta < 90 degrees are:

sin(theta) ≈ 0.9511

tan(theta) ≈ 0.3249

Therefore, the correct answer is A. sin(theta) = 0.9511; tan(theta) = 0.3249.

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To accurately complete the proof, the angles that can be filled in are: BCD and CDA; ABC and BAT.

Let's go step by step to understand why these angles are congruent. Given that segment AB is parallel to segment DC and segment BC is parallel to segment AD, we extend segment AB to point P above point B and extend segment AD to point T to the left of point A.

According to the Alternate Interior Angles Theorem, angles BCD (angle at point C) and CDA (angle at point D) are congruent. This is because these angles are formed by a transversal (segment AD) intersecting two parallel lines (AB and DC).

Next, applying the Corresponding Angles Theorem, angles ABC (angle at point A) and BAT (angle at point T) are congruent. This is because these angles are corresponding angles formed by a transversal (segment AB) intersecting two parallel lines (AD and BC).

By the Transitive Property of Equality, we can conclude that angle ABC is congruent to angle CDA. Therefore, opposite angles of parallelogram ABCD are congruent, and the proof is complete.

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Answer:

38.7

Step-by-step explanation:

[tex]\frac{sinA}{A}=\frac{sinB}{B}=\frac{sinC}{C}[/tex]

A, B and C are the sides of the triangle and sinA, sinB and sinC are the opposing angles

[tex]\frac{sin95}{43}=\frac{A}{27}[/tex]

[tex]A = sin^{-1} (\frac{27*sin95}{43} )=38.72018809[/tex]

Answer:

Square.

Step-by-step explanation:

A square is a rectangle, but a rectangle is not a square.

Answer:

A square

Step-by-step explanation:

The file below can help you out understand the properties of the square better!

The answer that you are looking for is b) 5(a – 2)(a – 4). In order to factor the formula, we must first locate two numbers whose sum is equal to -30 and whose product is equal to 40. Both constraints are met by the values -4 and -10, and as a result, we are able to factor the statement as 5(a – 2)(a – 4).(option b)

The following procedures can be used by us while factoring polynomials:

Find two numbers that, when added together, give you the coefficient of the middle term, and then multiply those two values by themselves to get the constant term.

Create the expression as the product of two binomials, with each binomial having one of the two numbers discovered in step 1. Write the equation as a product of two binomials.

Eliminate any factors that are frequent.

In this particular instance, the coefficient of the intermediate term is -30, while the value of the constant term is 40. When added together, the numbers -4 and -10 equal -30, and when multiplied together, they equal 40. Therefore, the expression can be factored as 5(a minus 2)(a minus 4).

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Answer:

159.4

Step-by-step explanation:

I'm assuming that it's supposed to be 15x^3-12x^2 because when you copy and paste the "^" gets cut out

15*2.5^3 - 12*2.5^2 = 234.375 - 75 = 159.375

rounded is 159.4

Answer:

4x - 3.4xy

Step-by-step explanation:

x(4 - 3.4y)

4x - 3.4xy

While factoring the given equation, the mistake occurred in Step 1 (option d.)

Upon reviewing the steps, we can see that the student made a mistake in Step 1. The factorization of the polynomial should be (x + 5)(x + 9), not (x + 5)(x - 9).

The correct factorization should be:

[tex]x^2 + 14x + 45 = (x + 5)(x + 9)[/tex]

The mistake occurred when the student incorrectly wrote (x - 9) instead of (x + 9) as one of the factors.

As a result, the subsequent steps are also affected. In Step 2, the student incorrectly set x - 9 = 0 instead of x + 9 = 0. This leads to an incorrect value in Step 3, where the student states that x = 9 instead of the correct value x = -9.

Therefore, the student made a mistake in Step 1, which caused subsequent errors in Step 2 and Step 3. The correct answer is d. The mistake occurred in Step 1.

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Answer:

15.98cm

Step-by-step explanation:

Given data

Volume= 602.88cm^3

Radius= 6cm

The formula for the volume of a cone is

V= 1/3 πr^2h

substitute

602.88= 1/3*3.142*6^2*h

602.88=1/3*3.142*36*h

602.88=37.704*h

h= 602.88/37.704

h= 15.98cm

Hence the height is 15.98cm

Answer:

Step-by-step explanation:

There are 12 marbles in total with three of them being striped. The chance of pulling out a striped marble is 3/12 which can be reduced to 1/4. And 1/4 of 600 is 150.

The probability that the next student he sees will be a boy with brown eyes is 25%. All of them are the exact same so 100 divided by 4 is 25.

The perimeter of the wood deck can be expressed, based on the length and width of the swimming pool to be 80 + 8c + 8w feet.

The perimeter of a rectangle is given by the formula 2x ( length + width ). With the walkway installed, the length becomes (28 + 2c) feet and the width becomes ( 12 + 2c ) feet.

Therefore, the length with the wood deck is ( 28 + 2c + 2w ) feet and the width with the deck is ( 12 + 2c + 2w ) feet.

The perimeter would therefore be:

P = 2 x [ ( 28 + 2c + 2w ) + (12 + 2c + 2w )]

P = 2 x [ 40 + 2c + 2w + 2c + 2w ]

P = 80c + 8 c + 8 w

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Answer

328,268.2 mm cubed is correct!

Step-by-step explanation:

If you use the formula V=πr²h with these steps:

1. Calculate the area of the base (which is a circle)

2. use the equation πr² where r is the radius of the circle.

3. Then, multiply the area of the base by the height of the cylinder

4. The volume is found!

Answer:

328,268.2 cubic millimeters

Step-by-step explanation:

I did it on edge

Answer:

its C

Step-by-step explanation:

Answer:

c. I believe

Step-by-step explanation:

because all of the other options dont go in a consistent order/pattern. C. matches the vertical side

please consider marking me as brainliest. as I explained my answer!

Please and thanks!

Answer:

184 in²

Step-by-step explanation:

Given :

Width, w = 6 inches

Length, l = 10 inches

Height, h = 2 inches

To obtain how much wrapping paper is needed ; we take the surface area of the box

Surface area = 2(lw + lh + wh)

Surface area = 2((6*10) + (6*2) + (10*2))

Surface area = 2(60 + 12 + 20)

Surface area = 2(92)

Surface area = 184 in²

The amount of wrapping paper needed = 184 in²

a) The expression for total revenue is:

[tex]R(x) = \int MR(x) dx = \int (205 -0.5x^2) dx = 205x - 0.25x^3[/tex]

The demand function is:

[tex]x = R^{-1}(R) = \frac{205}{0.25R + 1}[/tex]

b) The expression for the total cost function is:

[tex]C(x) = \int MC(x) dx = \int (85 +0.7x^2) dx = 85x + 0.21x^3 + 10[/tex]

c)The maximum profit, is 1079.56

a) Total revenue is the integral of marginal revenue. Thus, expression for total revenue is:

[tex]R(x) = \int MR(x) dx = \int (205 -0.5x^2) dx = 205x - 0.25x^3[/tex]

The demand function is the inverse of the total revenue function:

[tex]x = R^{-1}(R) = \frac{205}{0.25R + 1}[/tex]

b) Total cost is the integral of marginal cost:

[tex]C(x) = \int MC(x) dx = \int (85 +0.7x^2) dx = 85x + 0.21x^3 + 10[/tex]

c) Profit is total revenue minus total cost:

P(x) = R(x) - C(x) = 205x - 0.25x³ - (85x + 0.21x³ + 10) = 120x - 0.46x³ - 10

To find the maximum profit, we need to find the point where marginal profit is zero. Marginal profit is the derivative of profit:

P'(x) = 120 - 1.38x² = 0

Solve for x:

120 - 1.38x² = 0

1.38x²  = 120

x² = 120/1.38

x = √(120/1.38)

x = 9.33

We find that the maximum profit is achieved when x = 9.33. Thus, the maximum profit:

P(9.33) = 120(9.33) - 0.46(9.33)³ = 1079.56

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Answer:

-12n - 6

Step-by-step explanation: